Performance Comparison of Ferrite and Nanocrystalline Cores for Medium-Frequency Transformer of Dual Active Bridge DC-DC Converter

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Article Performance Comparison of Ferrite and Nanocrystalline Cores for Medium-Frequency Transformer of Dual Active Bridge DC-DC Converter

Sakda Somkun 1,* , Toshiro Sato 2, Viboon Chunkag 3, Akekachai Pannawan 1, Pornnipa Nunocha 1 and Tawat Suriwong 1

1 School of Renewable Energy and Smart Grid Technology (SGtech), Naresuan University, Phitsanulok 65000, Thailand; [email protected] (A.P.); [email protected] (P.N.); [email protected] (T.S.) 2 Department of Electrical and Computer Engineering, Shinshu University, Nagano 380-8553, Japan; [email protected] 3 Department of Electrical and Computer Engineering, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand; [email protected] * Correspondence: [email protected]

Abstract: This article reports an investigation into ferrite and nanocrystalline materials for the medium-frequency transformer of a dual active bridge DC-DC converter, which plays a key role in the converter’s efficiency and power density. E65 MnZn ferrite cores and toroidal and cut nanocrystalline cores are selected for the construction of 20-kHz transformers. Transformer performance is evaluated with a 1.1-kW (42–54 V)/400 V dual active bridge DC-DC converter with single-phase shift and extended phase shift modulations. The experimental results indicate that the toroidal nanocrystalline Citation: Somkun, S.; Sato, T.; transformer had the best performance with an efficiency range of 98.5–99.2% and power density of Chunkag, V.; Pannawan, A.; 3 Nunocha, P.; Suriwong, T. 12 W/cm , whereas the cut-core nanocrystalline transformer had an efficiency range of 98.4–99.1% 3 Performance Comparison of Ferrite with a power density of 9 W/cm , and the ferrite transformer had an efficiency range of 97.6–98.8% 3 and Nanocrystalline Cores for with a power density of 6 W/cm . A small mismatch in the circuit parameters is found to cause Medium-Frequency Transformer of saturation in the nanocrystalline toroidal core, due to its high permeability. The analytical and Dual Active Bridge DC-DC Converter. experimental results suggest that cut nanocrystalline cores are suitable for the dual active bridge Energies 2021, 14, 2407. https:// DC-DC converter transformers with switching frequencies up to 100 kHz. doi.org/10.3390/en14092407 Keywords: dual active bridge DC-DC converters; ferrite material; nanocrystalline material; soft Academic Editor: Mario Marchesoni magnetic material; transformer

Received: 13 March 2021 Accepted: 20 April 2021 Published: 23 April 2021 1. Introduction

Publisher’s Note: MDPI stays neutral A dual active bridge (DAB) DC-DC converter, shown in Figure1, is widely employed with regard to jurisdictional claims in in modern electrical power generation and distribution systems for bidirectional power published maps and institutional affil- transfer between two DC sources with galvanic isolation [1]. DAB DC-DC converters are iations. normally applied in solid-state transformers (SSTs) for photovoltaic and wind energy systems [2–4], on-board battery chargers in electric vehicles [5], railway traction systems [6,7], electric aircraft applications [8], and grid energy storage systems [9–12]. The transformer of the DAB DC-DC converter is a key component that has a direct impact on converter performance. The switching frequency of the DAB DC-DC converter is Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. normally in the medium frequency range, between a few kHz [13] to hundreds of kHz [5]. This article is an open access article Transformer losses depend on the operating frequency, core materials, peak flux density, distributed under the terms and and winding configurations. Core materials with high saturation flux density and low conditions of the Creative Commons loss at higher operating frequency result in high power density. Applications of soft Attribution (CC BY) license (https:// magnetic materials for power conversion have been thoroughly surveyed and summarized creativecommons.org/licenses/by/ by the authors of [14]. Silicon steels are typically used in high power applications with an 4.0/). operating frequency of approximately 1 kHz [13,15,16], due to high peak flux density, and

Energies 2021, 14, 2407. https://doi.org/10.3390/en14092407 https://www.mdpi.com/journal/energies Energies 2021, 14, x FOR PEER REVIEW 2 of 22

Energies 2021, 14, 2407 2 of 21 magnetic materials for power conversion have been thoroughly surveyed and summarized by the authors of [14]. Silicon steels are typically used in high power applications with an operating frequency of approximately 1 kHz [13,15,16], due to high peak flux lowdensity, material and cost.low material Ribbon-wound cost. Ribbon-woun amorphous coresd amorphous are employed cores atare operating employed frequencies at operat- belowing frequencies 10 kHz [17 below], due 10 to kHz a lower [17], core due lossto a thanlower silicon core loss steels. than The silicon application steels. The of ferrite appli- corescation for of DABferrite DC-DC cores for converter DAB DC-DC transformers converter dominates transformers frequency dominates ranges frequency between 5ranges kHz tobetween 500 kHz 5 kHz [5,7, 8to,18 500–20 kHz]. However, [5,7,8,18–20]. iron-based However, ribbon-wound iron-based nanocrystallineribbon-wound nanocrystal- cores have becomeline cores competitive have become with competitive ferrite cores with inthe ferrite frequency cores in range the frequency of 5 kHz uprange to 100of 5 kHz kHz [ 4up]. Ribbon-woundto 100 kHz [4]. Ribbon-wound nanocrystalline nanocrystalline cores exhibit a lowercores exhibit specific a corelower loss specific and a core higher loss peak and fluxa higher density peak compared flux density to ferritecompared cores, to ferrite leading cores, to greater leading power to greater density power and density efficiency. and Moreover,efficiency. coreMoreover, loss of core the loss ferrite of the material ferrite varies material with varies core with temperature, core temperature, due to a lowerdue to Curiea lower temperature Curie temperature compared compared to other materials.to other materials.

Figure 1. Application of DAB DC-DC converters in electricity generation and distribution systems. Figure 1. Application of DAB DC-DC converters in electricity generation and distribution systems.

SeveralSeveral studiesstudies havehave focusedfocused onon thethe designdesign andand performanceperformance evaluationevaluation ofof thethe trans-trans- formerformer ofof thethe DABDAB DC-DCDC-DC converter.converter. SiliconSilicon steelssteels andand nanocrystallinenanocrystalline materialsmaterials werewere comparedcompared forfor thethe constructionconstruction of 1-kVA 120120 V/240 V V transformers transformers operating operating under under at at 1 1kHz kHz [21], [21], in in which which reported reported the the silicon steel transformer was reportedreported toto exhibitexhibit muchmuch lower efﬁciency and power density than the nanocrystalline core. Nonetheless, the advan- tage of the nanocrystalline materials over the silicon steels cannot be justiﬁed in this work, since the silicon steel transformer was tested under a reduced power rating. P. Huang [22]

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reported on the design and construction of a 1.5-kV, 35-kW, 1-kHz transformer for a DAB DC-DC converter using a 0.18-mm thick silicon steel, which was compared with an amorphous transformer with a similar rating. It was found that the silicon steel transformer exhibited a considerably greater no-load loss (i.e., greater core loss) with a slightly higher power density than the amorphous transformer. Note that the on-load test of the transformers was conducted by the authors of [22] with a full bridge rectifier at the secondary winding, rather than an active bridge. Researchers from Gazi University, Turkey, compared N87 MnZn ferrite material from TDK Electronics AG with a cut ribbon wound nanocrystalline core for a 35-kVA 10-kHz transformer under a square wave voltage excitation [18]. The finite element analysis (FEA) results indicate that the nanocrystalline transformer has a lower total loss and better power density than the ferrite transformer. A prototype of the nanocrystalline transformer was constructed [23], with the total experimental loss found to tend to be greater than that obtained from the FEA. The total experimental loss was found to be 120 W under a resistive load of 6 kW, whereas the total loss from the FEA was calculated at 155 W under a resistive load of 35 kW. Three configurations (toroidal, C cores with the core type winding, and C cores with shell type winding) of 1750-VA 5-kHz transformers were constructed from Vitroperm500F nanocrystalline cores [24]. The toroidal configuration exhibited the highest efficiency at 98.5% and the highest magnetizing inductance, whereas the core type structure had the lowest efficiency at 96%. The core type transformer has the highest leakage inductance, which is suitable for the DAB DC-DC converter application. A multi-objective design method for 10-kVA 20-kHz transformers for LLC DC-DC resonant converters and DAB DC-DC converters using a genetic algorithm was presented [19]. The two transformers were constructed on E100/60/28 cores of the 3C90 MnZn ferrite material. The calculated efficiency for the DAB DC-DC converter transformer was claimed at 99.31% and 99.43% for the LLC DC-DC converter transformer. However, no experimental efficiency was reported. The improved generalized Steinmetz equation (iGSE) was applied in an optimized design methodology of a 1-MW 3 kV/6 kV 5-kHz transformer with thermal and dielectric, and thermal considerations [25]. The optimized result suggests that using the Vitrop- erm500F nanocrystalline material in the transformer core exhibited better efficiency and power density than using the 3C95 MnZn ferrite. The proposed design methodology was validated with a down-scaled prototype using the 3C95 ferrite material, which was tested under open-circuit and short-circuit measurements for efficiency evaluation. M. Mogorovic and D. Dujic [26] presented a design methodology for a 100-kW 10-kHz transformer for a medium voltage LLC DC-DC resonant converter. The prototype transformer, constructed with N87 SIFERRIT ferrite U-cores was evaluated to have an efficiency above 99.3% at the rated condition. Other aspects of MF transformer design are leakage inductance modeling, local electric field distribution inside the transformer [27], and inductor-integrated MF transformer design [20]. As mentioned above, no studies have compared experimental performance with different core materials under the same operating conditions in a DAB DC-DC converter. Moreover, the prototype transformers in the literature were mostly tested or evaluated at the rated condition. In some applications, for example, the battery application [10], one of the DC voltage sides of the DAB DC-DC converter is not constant. The battery voltage varies with the state of charge, which directly impacts the operating performance of the MF transformer, i.e., flux density and core losses. In this work, we report our investigation through a performance comparison of DAB DC-DC converter transformers constructed from an MnZn ferrite core and ribbon-wound nanocrystalline cores. Three prototype transformers were tested with a 1.1-kW 20-kHz DAB DC-DC converter. The test conditions were performed under different peak flux densities, which are suitable for battery applications. Energies 2021, 14, x FOR PEER REVIEW 4 of 22

Energies 2021, 14, 2407 DAB DC-DC converter. The test conditions were performed under different peak4 offlux 21 densities, which are suitable for battery applications.

2.2. DAB DC-DC Converter in This Study Figure2 2 depicts depicts thethe DAB DAB converter converter inin this this study study which which can can be be used used to to integrate integrate a a lithium-ionlithium-ion batterybattery with with a a single-phase single-phase AC AC grid. grid. The The DAB DAB DC-DC DC-DC converter converter is operatedis operated at aat switching a switching frequency frequency of 20 of kHz. 20 kHz. The lowThe voltagelow voltage (LV) bridge(LV) bridge is connected is connected to a DC to power a DC supplypower supply to emulate to emulate a battery a packbattery in dischargingpack in discharging mode where mode the where battery the voltage batteryVB voltagevaries in the varies range in the of 42–54 rangeV of with 42–54 the V nominalwith the voltagenominalV voltageBn = 48 V. This = 48 topology V. This topology is suitable is forsuitable testing for the testing prototype the prototype transformers, transformers, since the since core the ﬂux core density flux variesdensity with varies the with battery the voltagebattery andvoltage the primaryand the primary voltage waveform.voltage waveform. The DC sideThe ofDC the side high of voltagethe high (HV) voltage bridge (HV) is connectedbridge is connected to the DC busto the of theDC voltagebus of the source voltage converter source (VSC) converter connected (VSC) to connected a 220-V, 50-Hz to a single-phase220-V, 50-Hz gridsingle-phase through angrid LCL through ﬁlter. Thean LCL DC busfilter. voltage The DCVD busof thevoltage VSC is regulated of the VSC at 400is regulated V. An auxiliary at 400 inductorV. An auxiliaryLa, to limit inductor the transferred , to limit power, the transferred is placed on power, the HV is side placed for easeon the of construction,HV side for ease due of to aconstruction, smaller current. due Theto a transformersmaller current. turn ratioThe transformer is set at turn ratio is set at N V 2 = D (1) N1 =VBn (1) where N and N are the turn number of the primary and secondary windings. Thus, the 1 2 voltagewhere conversion and areratio thed isturn given number by of the primary and secondary windings. Thus, the voltage conversion ratio is given by N1 VD VBn d == == (2) N2 VB VB (2) 2

Dual Active Bridge DC-DC Converter Grid-connected Inverter i B i1 i2 iD MF Transformer

Llk1 Llk2 La L 220 V, 50 Hz ip is iinv f Lg ig VB = 48 V C2 Grid C1 + + v vsc p vs V vc C (42-54 V) D f vg

N1 N2

FigureFigure 2.2. DAB DC-DC converter in thisthis study.study.

Figure3 3aa illustrates illustrates the the key key waveformswaveforms of of thethe DABDAB DC-DCDC-DC converterconverter withwith thethe single-single- phasephase shiftshift (SPS) modulation strategy [[28],28], where the fluxflux density waveform is triangular. UnderUnder this SPS modulation, the voltage conversion ratio ratio d should shouldbe be maintainedmaintained closeclose toto unityunity toto satisfysatisfy the the zero-voltage zero-voltage switching switching (ZVS) (ZVS) condition condition for for efficient efficient power power transfer. transfer. The extendedThe extended phase phase shift (EPS)shift (EPS) modulation modulation is applied is applied at a higher at a higher battery battery voltage voltage level where level thewhere primary the primary voltage voltage is modulated is modulated with the with duty the ratio dutym, asratio shown , as in shown Figure 3inb. Figure This EPS 3b. modulationThis EPS modulation was reported was reported to enhance to enhance the ZVS the range ZVS and range reduce and reduce the current the current stress instress the transformerin the transformer windings, windings, in addition in addition to transformer to transformer losses losses [28]. The[28]. fluxThe densityflux density waveform wave- underform under this EPS this modulation EPS modulation is trapezoidal, is trapezoidal, as illustrated as illustrated in Figure in Figure3b, which 3b, which affects affects the transformerthe transformer core loss.core Referringloss. Referring to the to LV the side LV of theside transformer, of the transformer, the transferred the transferred power is givenpower by, is given by, 2 2 2 2 2 1 VB d 2δmπ − 2δ − m π + mπ P1 = 1 2 − 2 − + (3) =2 πωs Lat (3) 2 where ωs = 2π fs is the switching angular frequency, and Lat is the total leakage inductor where =2 is the switching angular frequency, and is the total leakage induc- with the auxiliary inductor [28]. The RMS current Ip of the primary winding is necessary informationtor with the forauxiliary the design inductor of the [28]. transformer The RMS [current28], which of is expressedthe primary as, winding is necessary information for the design of the transformer [28], which is expressed as, r V 2 3 B 2 3 2 3 2 2 3 Ip = πω L 3π d π + 12δ mπd − 8dδ + 12δdmπ − 6mdπ − (12dδ)(mπ) + 4d(mπ) + 3π (4) = 6 s at3 + 12 − 8 + 12 −6 − 12 +4 +3 (4) 6

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Neglecting voltage drops across the MOSFETs, the peak ﬂux density in the transformer coreNeglecting is approximately voltage drops proportional across the to theMOSFETs, battery voltagethe peakV Bflux density in the transformer core is approximately proportional to the battery voltage Z Ts/2 ˆ 1 mVBTs B = /vpdt = (5) 2N=Ac 0 =4N Ac (5) 1 1

wherewhereA cis is the the cross-sectional cross-sectional area area of of the the transformer transformer core. core.

(a) (b)

FigureFigure 3. 3.Key Key waveforms waveforms of of the the DAB DAB DC-DC DC-DC converter converter in in this this study: study: (a ()a The) The SPS SPS modulation; modulation; (b ()b the) the EPS EPS modulation. modulation.

TableTable1 summarizes1 summarizes the the parameters parameters of of the the DAB DAB DC-DC DC-DC converter converter in in this this study. study.

TableTable 1. 1.Parameters Parameters of of the the DAB DAB DC-DC DC-DC converter. converter.

ParametersParameters ValuesValues Battery voltage, 42–54 V Battery voltage, VB 42–54 V Nominal battery battery voltage, voltage,VBn 48 V 48 V DC busbus voltage,voltage,V D 400 V 400 V Switching frequency, fs 20 kHz Switching frequency, 20 kHz Nominal power at VBn 1100 W Nominal power at 1100 W Maximum power at VB = 54 V 1200 W ◦ MaximumPhase shift angle,powerδ at = 54 V 0–60 1200 W PhaseDuty ratio, shiftm angle, 0.7–1.00–60° DutyTotal inductanceratio, Lat referred to N2 808 µH0.7–1.0 Nominal primary RMS current, Ip at VBn and m = 1.0 30.3 A Total inductance referred to 808 µH Input capacitor, C1 3 mF NominalDC bus capacitor, primaryC 2RMS current, at and = 1.0 3.3 mF30.3 A InputLV bridge capacitor, MOSFETs IXYS IXFN 140N20P3 mF HV bridge IGBTs Inﬁneon FF50R12RT4 DC bus capacitor, 3.3 mF LV bridge MOSFETs IXYS IXFN 140N20P 3.HV Design bridge and IGBTs Construction of the MF Transformers Infineon FF50R12RT4 N87 MnZn ferrite material from EPCOS [29] and two nanocrystalline materials from MK3. Design magnetics and [ 30Construction], with 17-µ mof thickthe MF ribbons, Transformers and King Magnetics [31], with 20-µm thick ribbonsN87 were MnZn selected ferrite in thismaterial study from for the EPCOS construction [29] and of two three nanocrystalline prototype transformers, materials duefrom toMK their magnetics commercial [30], availability. with 17-µm Table thick2 compares ribbons, and the keyKing parameters Magnetics of [31], the N87with ferrite 20-µm with thick theribbons two nanocrystalline were selected materials.in this study Loss for densities the construction of the selected of three materials prototype were transformers, reproduced fromdue theto their manufactures’ commercial data availability. using the Table GSE. Figure2 compares4a shows the key that parameters the two nanocrystalline of the N87 ferrite with the two nanocrystalline materials. Loss densities of the selected materials were

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Energies 2021, 14, 2407 6 of 21 reproduced from the manufactures’ data using the GSE. Figure 4a shows that the two nanocrystalline materials have loss densities lower than that of the N87 ferrite material at fmaterialss = 20 kHz. have However, loss densities the N87 lower ferrite than material that of exhibits the N87 a ferritesmaller material loss density at fs = at 20 kHz. = 0.30 How- T forever, the the frequency N87 ferrite above material 200 kHz, exhibits as illustrated a smaller lossin Figure density 4b. at TheBˆ = King 0.30 Tmagneticsfor the frequency nano- crystallineabove 200 material kHz, as illustratedhas a lower in loss Figure density4b. Thethan King the MK magnetics magnetics nanocrystalline for < 0.7 T materialand fs < 60has kHz. a lower However, loss density the eddy than current the MK loss, magnetics due to forthe Bˆthicker< 0.7T ribbon and fs of< 60the kHz. King However, magnetics the nanocrystallineeddy current loss, material, due to thecauses thicker the loss ribbon dens ofity the to King be greater magnetics than nanocrystalline that of the MK material, mag- neticscauses nanocrystalline the loss density material to be greater at a higher than that peak of flux the MKdensity magnetics and magnetizing nanocrystalline frequency. material at a higher peak ﬂux density and magnetizing frequency. Table 2. Key parameters of the transformer core materials.

Table 2. Key parameters of the transformer core materials.Core Materials Parameters Nanocrystalline, MK Nanocrystalline, N87 Ferrite Core Materials Magnetics King Magnetics Parameters Nanocrystalline, Nanocrystalline, N87 Ferrite Saturation flux density, 0.39 T MK 1.23 Magnetics T King 1.25 Magnetics T Coercivity 21 A/m Not given 1.2 A/m Saturation ﬂux density, Bsat 0.39 T 1.23 T 1.25 T InitialCoercivity permeability 2200 21 A/m 60,000 Not given 80,000 1.2 A/m PhysicalInitial permeability density 4850 kg/m 22003 7300 kg/m 60,0003 7250 80,000kg/m3 CuriePhysical temperature density >2104850 kg/m°C 3 5707300 °C kg/m 3 7250 560 °C kg/m 3 ◦ ◦ ◦ SteinmetzCurie temperature parameter, 2.10 >210 C 2.10 570 C 2.38 560 C Steinmetz parameter, β 2.10 2.10 2.38 Steinmetz parameter, 1.36 1.44 1.64 Steinmetz parameter, α 1.36 1.44 1.64 SteinmetzSteinmetz parameter, parameter, K c 1.7661.766 0.6472 0.6472 0.101 0.101 [W/(m[W/(m3Hz3HzαTαβT)]β )]

(a)

(b)

Figure 4. Loss densities of the N87 ferrite material, and nanocrystalline materials from MK magnetics and King magnetics: (a) Peak ﬂux density from 0.01 T to 1.20 T at 20 kHz; (b) magnetizing frequency from 5 kHz to 300 kHz at 0.30 T. Energies 2021, 14, 2407 7 of 21

A well-established analytical method [32] was selected to design the MF transformers. This method optimizes the core size and peak ﬂux density constrained by the total allowable loss. The core loss is given by the generalized Steinmetz equation and the copper loss. All the parameters in this design methodology are referenced to the primary winding. Thus, the copper loss is calculated from the total RMS current referenced to the primary winding, Itot which is given by, Itot = Ip + N2/N1 Is (6)

where Is is the RMS secondary current. Neglecting the magnetizing current, Ip = N2/N1 Is. ∼ Thus, Itot = 2IP calculated from (4) was used in the design. The output of this design yields an optimal core size and an optimal peak flux density. From there, a transformer core was selected as close as possible to the optimal core. Each MF transformer was designed at the nominal battery voltage of 48 V with m = 1.0. The maximum allowable power loss at the nominal battery voltage of 48 V was set to 10 W, which is 0.91% of the rated power. The maximum peak flux density at the battery maximum voltage of 54 V with the duty ratio m = 1.0 was constrained to be lower than 50% of the saturation flux density, as presented in Table2. Table3 summarizes the parameters of the three prototype transformers, denoted as transformers A, B, and C. Core loss, copper loss, and total loss of each transformer were estimated during the design stage.

Table 3. Parameters of the prototype transformers.

Transformers Parameters ABC Material EPCOS N87 ferrite MK Magnetics nanocrystalline King Magnetics nanocrystalline Core structure 1 set of E65/32/27 2 sets of cut C-cores, SC2043M1 Toroid, KMN503220T 2 2 2 Total core area, Ac 5.29 cm 3.12 cm 1.4 cm Magnetic length, lm 14.7 cm 12.8 cm 12.9 cm 6 turns 7 turns 10 turns Primary winding 2 Litz wires (500 × AWG40) 1 Litz wire (800 × AWG40) 2 Litz wires (265 × AWG36) 50 turns 59 turns 83 turns Secondary winding 2 Litz wires (40 × AWG36) 1 Litz wires (128 × AWG40) 1 Litz wires (128 × AWG40) Bˆ at 48 V/54 V 0.19 T/0.21 T 0.27 T/0.31 T 0.43 T/0.48 T Est. Pcu at 48 V/54 V 3.3 W/4.8 W 3.8 W/5.5 W 4.0 W/5.8 W Est. Pf e at 48 V/54 V 6.7 W/9.2 W 2.7 W/3.5 W 2.7 W/3.6 W Est. Ptot at 48 V/54 V 10.0 W/15.0 W 6.5 W/9.0 W 6.7 W/9.4 W Lm1 0.26 mH 0.16 mH 5.46 mH µ µ µ Llkt,N2 22 H 9 H 43 H

Figure5 depicts core geometry, winding conﬁgurations, and photographs of the three transformers. Litz wires assembled from AWG36 and AWG40 conductors were used in the windings to minimize losses, due to as the skin effect and the proximity effect. The primary magnetizing inductance Lm1 and the total leakage inductance referred to the secondary

winding Llkt,N2 were determined using an LCR meter at 2 V 20 kHz. Nanocrystalline transformer C has the greatest magnetizing inductance Lm1, due to its highest initial permeability, as given in Table2. However, nanocrystalline transformer B has the lowest magnetizing inductance Lm1 despite its high initial permeability. This is believed to be due to the presence of air gaps and core deterioration during the cutting process. Energies 2021, 14, 2407 8 of 21 Energies 2021, 14, x FOR PEER REVIEW 8 of 22

(a)

(b)

(c)

FigureFigure 5. CoreCore geometry, geometry, winding winding configuration, conﬁguration, and and photographs photographs of the of theprototype prototype transformers transform- densities of the N87 ferrite material, and nanocrystalline materials from MK magnetics and King ers densities of the N87 ferrite material, and nanocrystalline materials from MK magnetics and magnetics: (a) Ferrite transformer A; (b) nanocrystalline transformer B; (c) nanocrystalline trans- King magnetics: (a) Ferrite transformer A; (b) nanocrystalline transformer B; (c) nanocrystalline former C. transformer C.

4.4. CoreCore LossLoss EvaluationEvaluation CoreCore lossloss measurementmeasurement inin thethe MFMF rangerange isis challenging.challenging. TheThe calorimetriccalorimetric conceptconcept isis regardedregarded as as the the most most accurate accurate method method [33 [33],], but but this this method method is time-consuming is time-consuming and requires and re- aquires special a special test chamber. test chamber. Moreover, Moreover, the measured the measured loss is not loss only is not the only core loss,the core but loss, also thebut copperalso the loss copper and loss other and losses other in losses the chamber. in the chamber. Furthermore, Furthermore, the calorimetric the calorimetric method method is not suitableis not suitable for temperature-dependent for temperature-dependent materials, ma suchterials, as ferrite. such as The ferrite. Watt-meter The Watt-meter method is moremethod convenient is more andconvenient is widely and used is widely for loss used measurement for loss measurement of inductors andof inductors transformers and intransformers power converters in power [34 ].converters With this method,[34]. With core this loss method, is calculated core loss from is measurements calculated from of themeasurements magnetizing of current the magnetizing in the primary current winding in the and primary the induced winding voltage and the in theinduced secondary volt- winding.age in the Measurement secondary winding. accuracy Measurement is difﬁcult to accuracy evaluate andis difficult was frequently to evaluate not and supplied was fre- in thequently existing not literaturesupplied [in34 the–36 existing]. literature [34–36]. A 1-MHz Yokogawa WT3000E power meter [37] was selected to measure core losses of the prototype transformers. Figure 6 depicts the open-circuit test to determine core

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losses . This setup is essentially identical to the Watt-meter method with guaranteed measurement accuracy. The primary winding of each transformer was excited by the LV bridge with the peak voltage in the primary winding approximately equal to the battery voltage , which was in the range of 42 V to 54 V and the duty ratio of 0.7 ≤ m ≤ 1.0. The primary current is fed to an internal shunt resistor of the power meter, and the secondary voltage is used as the measured voltage. The measured power is

1 1 = ∙ = ∙ (7) The core loss is then determined from

1 Energies 2021, 14, 2407 = = ∙ 9 of(8) 21 The power measurement accuracy for the WT3000E power meter is stated at ±(0.3% of reading + 0.2% of range) in the frequency between 10–50 kHz for the sinusoidal input A 1-MHz Yokogawa WT3000E power meter [37] was selected to measure core losses waveforms [37]. The measurement range for was selected at 600 V, whereas the meas- of the prototype transformers. Figure6 depicts the open-circuit test to determine core urement range for varied between 1 A and 5 A. The power measurement range was losses P . This setup is essentially identical to the Watt-meter method with guaranteed between f600 e W to 3000 W. According to the readings of , the core loss measurement measurement accuracy. The primary winding of each transformer was excited by the LV accuracy was approximated between ±(3–8)% for ferrite transformer A, ±(20–40)% for bridge with the peak voltage Vˆp in the primary winding approximately equal to the battery nanocrystalline transformer B, and ±(15–20)% for nanocrystalline transformer C. The esti- voltage VB, which was in the range of 42 V to 54 V and the duty ratio of 0.7 ≤ m ≤ 1.0. The matedprimary accuracy current depended is fed to an on internal the indicated shunt resistorvalues and of the the power measurement meter, and ranges. the secondary The best measurement accuracy of each transformer occurred at the highest indicated value. The voltage is used as the measured voltage. The measured power Pmeas is poorest power measurement accuracy for transformer B was caused by using the 5-A measurement range, due 1toZ itsTs high magnetizing1 Zcurrent.Ts The approximateddB(t) accuracies Pmeas = vs(t)·ip(t)dt = ip(t)· N2 dt (7) were poorer than the calculatedTs 0 values to accountTs for0 the non-sinusoidaldt waveforms. Alt- hough the loss measurement accuracy is considerably poor, averaging of several meas- urementThe numbers core loss gives is then a reasonable determined tendency from of the loss in each material [38]. This measurement setup should be compared with theZ caTlorimetric method for accuracy evaluation. N1 1 s dB(t) However, this work providesPf e = a reasonablePmeas = comparisonip(t)· Nof1 the threedt transformer materials(8) N2 Ts 0 dt under the same setup.

FigureFigure 6. 6. TransformerTransformer core core loss loss measurement measurement setup. setup.

The power measurement accuracy for the WT3000E power meter is stated at ±(0.3% The induced voltage in the secondary winding was measured by a 100-MHz of reading + 0.2% of range) in the frequency between 10–50 kHz for the sinusoidal input differential probe, and the magnetizing current (t) was measured by a 50-MHz HI- OKIwaveforms 3273-50 [current37]. The probe. measurement Experimental range sign foralsvs werewas selectedrecorded at in 600 a 70-MHz V, whereas oscilloscope the mea- (ISO-TECHsurement range IDS1074B) for ip variedwith 1000 between data 1points A and per 5 A.cycle. The The power instantaneous measurement flux range density was between and magnetic 600 W to 3000field W. According can be calculated to the readings as follows, of Pmeas , the core loss measurement accuracy was approximated between ±(3–8)% for ferrite transformer A, ±(20–40)% for nanocrystalline transformer B, and ±(15–20)% for nanocrystalline transformer C. The estimated accuracy depended on the indicated values and the measurement ranges. The best measurement accuracy of each transformer occurred at the highest indicated value. The poorest power measurement accuracy for transformer B was caused by using the 5-A measurement range, due to its high magnetizing current. The approximated accuracies were poorer than the calculated values to account for the non-sinusoidal waveforms. Although the loss measurement accuracy is considerably poor, averaging of several measurement numbers gives a reasonable tendency of the loss in each material [38]. This measurement setup should be compared with the calorimetric method for accuracy evaluation. However, this work provides a reasonable comparison of the three transformer materials under the same setup. The induced voltage vs(t) in the secondary winding was measured by a 100-MHz differential probe, and the magnetizing current im1(t) (t) was measured by a 50-MHz HIOKI 3273-50 current probe. Experimental signals were recorded in a 70-MHz oscilloscope (ISO- Energies 2021, 14, 2407 10 of 21

TECH IDS1074B) with 1000 data points per cycle. The instantaneous ﬂux density B(t) and magnetic ﬁeld H(t) can be calculated as follows,

1 Z B(t) = vs(t)dt (9) N2 Ac

N1ip(t) H(t) = (10) lm The measured core losses were compared with the improved generalized Steinmetz equation (iGSE) [39], which is considered to be accurate for the non-sinusoidal ﬂux density waveforms, shown in Figure3. The core material parameters K f e, α and β in Table2 are adopted in the iGSE loss modeling, which is written as,

Z T α (Aclm) s dB β−α Pf e = ki (∆B) dt (11) Ts 0 dt

where, K f e ki = (12) α−1 R 2π α β−α (2π) 0 |cos θ| 2 dθ

Figure7 compares the measured core loss Pf e of ferrite transformer A and nanocrystalline transformers B and C with the predicted values using the GSE and iGSE models. Each indicated value is the average of 10 readings, and each reading was from the average of 256 switching cycles. The indicated peak flux density Bˆ of each transformer was calculated from the peak voltage Vˆp using (5). The peak voltage Vˆp was in the range of 42–54 V with a voltage step of 2 V. Figure8 compares the B-H curves of the three transformer cores at Vˆp = 54 V and m = 1.0. Large oscillation in the B-H curve of nanocrystalline transformer C is believed to be due to parasitic capacitance caused by large space between turns in the primary winding as illustrated in Figure5c, in addition to parasitic capacitance in the measuring probes. Moreover, transformer C has the largest magnetizing inductance and leakage inductance, as shown in Table3, which caused resonance at a lower frequency compared with transformers A and B. The parasitic capacitance can be minimized using a multi-section winding configuration [40] or separating the primary and secondary windings on opposite sides of the toroidal core [41]. The measured core losses and the predicted core losses from the iGSE model of the three transformers indicate that the duty ratio m has a direct impact on the core loss at the same peak flux density. A square wave excitation m = 1.0 resulting in a triangular flux density waveform in the core has a core loss lower than that under a quasi-square wave m < 1 with a higher peak voltage Vˆp where the flux density waveform is trapezoidal. This is because the triangular flux density has a fundamental flux density component smaller than that with the trapezoidal flux density waveform [42]. The measured core loss of the ferrite transformer core is greater than those of the other two nanocrystalline transformer cores B and C. This is confirmed by the widest hysteresis loop, as shown in Figure8. The measured core loss of ferrite transformer A is approximately three times greater than the predicted values. This is believed to be due to the temperature-dependent characteristic of the N87 ferrite. The core material parameters K f e, α and β of the N87 ferrite were derived from the typical core loss values of the R34 toroids at 100 ◦C[29]. The measurements were taken in a 25 ◦C air-conditioned room where the core temperature was approximately 30 ◦C. According to the manufacturer’s data, the core loss of the N87 ferrite at 30 ◦C is approximately 60% greater than at 100 ◦C. Moreover, the segregated core structure of transformer A is expected to contribute greater loss than that of the lump configuration of the R34 toroid. Energies 2021, 14, x FOR PEER REVIEW 10 of 22

1 = (9)

= (10) The measured core losses were compared with the improved generalized Steinmetz equation (iGSE) [39], which is considered to be accurate for the non-sinusoidal flux density waveforms, shown in Figure 3. The core material parameters , and in Table 2 are adopted in the iGSE loss modeling, which is written as, = Δ (11) where,

= (12) | | 2 cos 2

Figure 7 compares the measured core loss of ferrite transformer A and nanocrystalline transformers B and C with the predicted values using the GSE and iGSE models. Each indicated value is the average of 10 readings, and each reading was from the average of 256 switching cycles. The indicated peak flux density of each transformer was calculated from the peak voltage using (5). The peak voltage was in the range of 42– 54 V with a voltage step of 2 V. Figure 8 compares the B-H curves of the three transformer cores at = 54 V and m = 1.0. Large oscillation in the B-H curve of nanocrystalline transformer C is believed to be due to parasitic capacitance caused by large space between turns in the primary winding as illustrated in Figure 5c, in addition to parasitic capacitance in the measuring probes. Moreover, transformer C has the largest magnetizing inductance and leakage inductance, as shown in Table 3, which caused resonance at a lower frequency compared with transformers A and B. The parasitic capacitance can be minimized using a multi-section winding configuration [40] or separating the primary and secondary windings on opposite sides of the toroidal core [41]. The measured core losses and the predicted core losses from the iGSE model of the three transformers indicate that the duty ratio m has a direct impact on the core loss at the same peak flux density. A square wave excitation m = 1.0 resulting in a triangular flux density waveform in the core has a core loss lower than that under a quasi-square wave Energies 2021, 14, 2407 m < 1 with a higher peak voltage where the flux density waveform is trapezoidal.11 This of 21 is because the triangular flux density has a fundamental flux density component smaller

Energies 2021, 14, x FOR PEER REVIEWthan that with the trapezoidal flux density waveform [42]. 11 of 22

Energies 2021, 14, x FOR PEER REVIEW 11 of 22

(a)

(b)

(b) (c) Figure 7. The core loss of the prototype transformers: (a) Ferrite transformer A; (b) nanocrystalline C-core transformer B; (c) nanocrystalline toroidal transformer C.

The measured core loss of the ferrite transformer core is greater than those of the other two nanocrystalline transformer cores B and C. This is confirmed by the widest hysteresis loop, as shown in Figure 8. The measured core loss of ferrite transformer A is approximately three times greater than the predicted values. This is believed to be due to the temperature-dependent characteristic of the N87 ferrite. The core material parameters , and of the N87 ferrite were derived from the typical core loss values of the R34 toroids at 100 °C [29]. The measurements were taken in a 25 °C air-conditioned room where the core temperature(c) was approximately 30 °C. According to the manufacturer’s data, the core loss of the N87 ferrite at 30 °C is approximately 60% greater than at 100 °C. Figure 7. The core loss of the prototype transformers: (a) Ferrite transformer A; (b) nanocrystalline FigureMoreover, 7. The the core segregated loss of the prototypecore structure transformers: of transformer (a) Ferrite A transformeris expected A;to (contributeb) nanocrystalline greater C-core transformer B; (c) nanocrystalline toroidal transformer C. C-coreloss than transformer that of B;the (c )lump nanocrystalline configuration toroidal of the transformer R34 toroid. C. The measured core loss of the ferrite transformer core is greater than those of the other two nanocrystalline transformer cores B and C. This is confirmed by the widest hysteresis loop, as shown in Figure 8. The measured core loss of ferrite transformer A is approximately three times greater than the predicted values. This is believed to be due to the temperature-dependent characteristic of the N87 ferrite. The core material parameters , and of the N87 ferrite were derived from the typical core loss values of the R34 toroids at 100 °C [29]. The measurements were taken in a 25 °C air-conditioned room where the core temperature was approximately 30 °C. According to the manufacturer’s data, the core loss of the N87 ferrite at 30 °C is approximately 60% greater than at 100 °C. Moreover, the segregated core structure of transformer A is expected to contribute greater loss than that of the lump configuration of the R34 toroid. Figure 8. B-H curves of the prototype transformers at = 54 V and m = 1.0. Figure 8. B-H curves of the prototype transformers at Vˆp = 54 V and m = 1.0.

Figure 8. B-H curves of the prototype transformers at = 54 V and m = 1.0.

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NanocrystallineNanocrystalline transformertransformer C C has has the the lowest lowest core core loss, loss, partly partly due due to its to smaller its smaller cross- sectional area . Another explanation is believed to be due to the toroidal core configu- cross-sectional area Ac. Another explanation is believed to be due to the toroidal core configuration,ration, which did which not did deteriorate not deteriorate during duringthe manufacturing the manufacturing process. process.This can Thisbe observed can be observedfrom the from highest the highestslope in slope the B-H in the curvesB-H curvesin Figure in Figure 8. Nanocrystalline8. Nanocrystalline transformer transformer B has Bthe has lowest the lowest slope slopein the inB-H the curve—B-H curve— even lower even than lower that than of ferrite that of transformer ferrite transformer A, which A,contradicts which contradicts the permeability the permeability values indicated values in indicated Table 3. inThis Table is considered3. This is consideredto be largely todue be to largely the presence due to theof gaps presence between of gaps the cores. between The the measured cores. The core measured loss of nanocrystalline core loss of nanocrystallinetransformer B transformeris approximately B is approximately 70% greater th 70%an the greater predicted than the value predicted at the valuelowest at peak the lowestflux density peak flux density= 42 V, mVˆp == 0.7, 42 V,andm =the 0.7, difference and the differenceis smaller iswith smaller higher with flux higher densities, flux densities,down to downapproximately to approximately 45% at the 45% highest at the highestpeak flux peak density flux density = 54V ˆV,p = m 54 = V,1.0.m Mean-= 1.0. Meanwhile,while, the measured the measured core loss core of loss nanocrystalline of nanocrystalline transformer transformer C is slightly C is slightly smaller smallerthan the thanpredicted the predicted values, where values, the where loss theerror loss difference error difference is between is between −0.1 W −to0.1 −0.8 W W. to −0.8 W. EddyEddy currentcurrent createdcreated byby short short circuits circuits between between the the ribbons ribbons is is considered considered a a major major causecause of of thethe excessexcess corecore lossloss and the low low permeability permeability of of nanocrystalline nanocrystalline transformer transformer B. B. A Acut cut surface surface of of an an MK MK magnetics magnetics SC2043M1 SC2043M1 na nanocrystallinenocrystalline C-core C-core used used in in transformer transformer B Bcores cores was was examined examined by by an an optical optical microscope microscope with with a amagnification magnification of of 100X, 100X, as as shown shown in inFigure Figure 9.9 It. Itis isevident evident that that there there are are possib possiblele short short circuit circuit paths paths for the for eddy the eddy current current circu- circulatinglating between between the adjacent the adjacent ribbons. ribbons. The surfac The surfacee short shortcircuits circuits could could be due be to due an tooxida- an oxidationtion reaction reaction of iron of on iron the on cut the surface cut surface during duringthe core the manufacturing core manufacturing process or process the trans- or theformer transformer construction construction process [36,42]. process Removal [36,42]. of Removal the surface of the short surface circuits short by etching circuits with by etchinga 40% ferric with achloride 40% ferric (FeCl3) chloride solution (FeCl3) can solution reduce can such reduce excessive such excessivecore loss core[36], lossalthough [36], althoughthis could this be couldimpractical be impractical for commercial for commercial production. production.

FigureFigure 9. 9.A A part part of of the the cut cut surface surface of anof MKan MK magnetics magnet SC2043M1ics SC2043M1 nanocrystalline nanocrystalline C-core C-core (transformer (trans- B). former B). 5. Operating Performance of the MF Transformers with the DAB DC-DC Converter 5. OperatingAn auxiliary Performance inductor of was the added MF Transformers to the secondary with windingthe DAB toDC-DC form theConverter required total leakageAn auxiliary inductance inductor close was to added 808 µ H,to the as givensecondary in Table winding1. This to allowedform the the required required total maximumleakage inductance power to be close limited. to 808 In µH, high as power given applications, in Table 1. This the required allowed leakage the required inductance maxi- ismum small, power where to thebe limited. design ofIn thehigh MF power transformer applications, with the integrated required leakage leakage inductance inductance is is possiblesmall, where [20,25 the,26]. design A 786- ofµH the inductor MF transformer wound on with ETD49 integrated N87 ferrite leakage cores inductance was connected is pos- tosible ferrite [20,25,26]. transformer A 786-µH A. Another inductor 765- woundµH inductor on ETD49 wound N87 ferrite on a paircores of was MK connected magnetics to SC2043M1ferrite transformer C-cores was A. selected Another for 765-µH the nanocrystalline inductor wound transforms on a B pair and C.of TheMK phase magnetics shift ◦ ◦ ◦ ◦ δSC2043M1was set at 15C-cores, 30 ,was 45 , selected and 60 ,for while the thenanocr batteryystalline voltage transformsVB was adjustedB and C. so The that phase the peak voltage Vˆp was maintained at the minimum 42 V, nominal 48 V and maximum 54 V shift was set at 15°, 30°, 45°, and 60°, while the battery voltage was adjusted so that values of the battery voltage. At Vˆp = 48 V and Vˆp = 54 V, the duty ratio m was adjusted the peak voltage was maintained at the minimum 42 V, nominal 48 V and maximum between 0.7 to 1.0. The primary and secondary side powers P1 and P2 were obtained from 54 V values of the battery voltage. At = 48 V and = 54 V, the duty ratio m was ad- the 1-MHz Yokogawa WT3000E power meter with the connection diagram depicted in justed between 0.7 to 1.0. The primary and secondary side powers and were ob- Figure 10. Total power loss P and efﬁciency η are determined as follows tained from the 1-MHz Yokogawaloss WT3000E power meter with the connection diagram depicted in Figure 10. Total power loss and efficiency are determined as follows Ploss = P2 − P1 (13) = − (13) P η = 2 (14) P1

Energies 2021, 14, x FOR PEER REVIEW 13 of 22

= (14)

The measured powers and occupied approximately 6% to 35% of the power

measurement range. The measurement accuracies of and ( and ) were approximated between ±(2–5)%, which were better than of in Section 3. Again, the approximated accuracies of and were conservative considering the non-sinusoidal waveforms. The accuracy of the efficiency can be then determined by the authors of [38],

= + (15)

Energies 2021, 14, 2407 Thus, the accuracy of the efficiency was approximated to be between ±(3–8)%13 of 21of the calculated values. Each reported value is the average of 10 readings, and each reading was from the average of 256 switching cycles.

FigureFigure 10.10. Transformer totaltotal lossloss measurementmeasurement setup.setup.

TheFigure measured 11 compares powers theP1 operatingand P2 occupied waveform approximatelys of the transformers 6% to 35% A-C of the with power the mea-DAB

surementDC-DC converter range. The at measurementthe nominal accuraciesbattery voltage of P1 and =P 248(ε V,P1 andm =ε 1.0,P2 )were and approximatedat the highest between ±(2–5)%, which were better than of P in Section3. Again, the approximated battery voltage = 54 V, m = 0.8 with correspondingf e peak flux densities indicated in the accuraciesfigure. Oscillations of P1 and inP2 thewere primary conservative voltage considering are believed the due non-sinusoidal to resonance waveforms.caused by para- The accuracysitic inductance of the efficiency and capacitanceεη can be of then the determinedLV bridge and by the the authors transformers. of [38], Minor current spikes appear in the primary current of ferriteq transformer A at 48 V, m = 1.0 as circled in 2 2 εη = ε + ε (15) Figure 11a, and the spikes disappear for a smallerP1 peakP2 flux density at 54 V, m = 0.8. Large current spikes in the primary current of nanocrystalline transformer C are found both at 48 V,Thus, m = 1.0 the and accuracy 54 V, m of = the 0.8, efficiency as circledε ηinwas Figure approximated 11c. These tophenomena be between are± caused(3–8)% by of theasymmetry calculated in values.the output Each voltage reported of the value LV isbr theidge, average due to ofa mismatch 10 readings, in device and each parameters reading waswhich from pushes the average the transformer of 256 switching cores close cycles. to saturation [36], which can be observed from the asymmetryFigure 11 compares in the B-H the of operating nanocrystalline waveforms transformer of the transformers C in Figure A-C8. Nanocrystalline with the DAB DC-DC converter at the nominal battery voltage Vˆp = 48 V, m = 1.0, and at the highest transformer C has a safety margin of − = 0.82 T at 48 V, m = 1.0—much larger than battery voltage Vˆp = 54 V, m = 0.8 with corresponding peak flux densities indicated in that of ferrite transformer A of − = 0.20 T. However, large permeability in nano- thecrystalline figure. Oscillationstransformer inC, thedue primary to its material voltage areproperties believed and due the to uncut resonance core causedstructure, by parasiticdrives the inductance flux density and interval capacitance close of to the sa LVturation bridge easily. and the Nanocr transformers.ystalline Minortransformer current B spikes appear in the primary current of ferrite transformer A at 48 V, m = 1.0 as circled in has the largest safety margin − = 0.98 T at 48 V, m = 1.0. Moreover, it has the lowest Figure 11a, and the spikes disappear for a smaller peak flux density at 54 V, m = 0.8. Large permeability, as observed from the B-H curve in Figure 8, due to the cut-core structure, current spikes in the primary current of nanocrystalline transformer C are found both at which together prevents saturation in the core. 48 V, m = 1.0 and 54 V, m = 0.8, as circled in Figure 11c. These phenomena are caused by Transformer core saturation can be passively prevented by adding air gaps [43] or asymmetry in the output voltage of the LV bridge, due to a mismatch in device parameters adding a DC-blocking capacitor in series with the primary winding of the transformer which pushes the transformer cores close to saturation [36], which can be observed from [44]. The volt-second imbalance can be actively compensated with a duty offset obtained the asymmetry in the B-H of nanocrystalline transformer C in Figure8. Nanocrystalline transformer C has a safety margin of Bsat − Bˆ = 0.82 T at 48 V, m = 1.0—much larger than that of ferrite transformer A of B − Bˆ = 0.20 T. However, large permeability in sat nanocrystalline transformer C, due to its material properties and the uncut core structure, drives the flux density interval close to saturation easily. Nanocrystalline transformer B has the largest safety margin Bsat − Bˆ = 0.98 T at 48 V, m = 1.0. Moreover, it has the lowest permeability, as observed from the B-H curve in Figure8, due to the cut-core structure, which together prevents saturation in the core. Transformer core saturation can be passively prevented by adding air gaps [43] or adding a DC-blocking capacitor in series with the primary winding of the transformer [44]. The volt-second imbalance can be actively compensated with a duty offset obtained from auxiliary magnetic cores [45], extra flux density sensors [46], or measurements of the transformer current slopes near the saturation boundaries [47]. The uncut toroidal structure has limited choices for the prevention of saturation in the core. Energies 2021, 14, x FOR PEER REVIEW 14 of 22

Energies 2021, 14, 2407 from auxiliary magnetic cores [45], extra flux density sensors [46], or measurements of14 ofthe 21 transformer current slopes near the saturation boundaries [47]. The uncut toroidal structure has limited choices for the prevention of saturation in the core.

(a)

(b)

(c)

FigureFigure 11. 11. OperatingOperating waveforms waveforms of of the the MF MF transfor transformersmers with the DAB DC-DC converter:converter: ((aa)) FerriteFer- ritetransformer transformer A; (A;b) ( nanocrystallineb) nanocrystalline C-core C-core transformer transformer B; ( cB;) nanocrystalline(c) nanocrystalline toroidal toroidal transformer trans- C. former C.

Figures 12–14 depict measurement results of the output power P2, power loss Ploss, totalFigures RMS current 12–14 Idepicttot and measurement efficiency η of results ferrite of transformer the output Apower and nanocrystalline, power loss trans-, totalformers RMS B andcurrent C at Vˆp = and 42,48, efficiency and 54 V with of ferrite the SPS transformer modulation Am =and 1.0. nanocrystalline At the nominal transformersoperating condition B and CVˆ pat= 48 V,= 42, nanocrystalline 48, and 54 V transformer with the SPS C exhibits modulation the best m = performance 1.0. At the nominalwith the operating highest power condition output of= 117148 V, W, nanocrystalline while 1132 W transformer for nanocrystalline C exhibits transformer the best performanceB and 1054 W with ferrite the transformerhighest power A. Itoutput can be of observed 1171 W, thatwhile the 1132 highest W for efficiency nanocrystalline of each transformercurve of the B three and transformers1054 W ferrite occurs transformer when the A. total It can loss beP observedloss approximately that the highest doubles effi- the ciencycore loss of Peachf e obtained curve of from the thethree measurement transformers results occurs in when Section the4. Notetotal thatloss the N87 approxi- ferrite ◦ ◦ matelydecreases doubles approximately the core inloss linear withobtained the core from temperature the measurement from 25 Cresults to 95 inC[ Section29]. Thus, 4. Notethe core that loss theP N87f e of ferrite transformerdecreases approxim A with theately DAB in linear DC-DC with converter the core is scaledtemperature to 70% fromof the 25 measured °C to 95 °C core [29]. loss, Thus, due the tothe core elevated loss temperature of ferrite transformer in the core A dissipated with the DAB from DC-DCthe winding. converter The is efficiency scaled to ranges 70% of of the the measured transformers core coverloss, due 97.6–98.5% to the elevated for ferrite temper- trans- atureformer in A,the 98.4–99.0% core dissipated for nanocrystalline from the winding. transformer The efficiency B, and 98.5–99.1% ranges of for the nanocrystalline transformers covertransformer 97.6–98.5% C. Copper for ferrite loss Ptransformercu dominates A, in 98 nanocrystalline.4–99.0% for nanocrystalline transformer C, transformer since the peak B, efficiency occurs at the light load δ = 15◦. This is due to the extra length of the primary winding, which distributes around the core, as illustrated in Figure5c.

Energies 2021, 14, x FOR PEER REVIEW 15 of 22

and 98.5–99.1% for nanocrystalline transformer C. Copper loss dominates in nano- and 98.5–99.1% for nanocrystalline transformer C. Copper loss dominates in nano- Energies 2021, 14, 2407 15 of 21 crystalline transformer C, since the peak efficiency occurs at the light load = 15°. This is due to the extra length of the primary winding, which distributes around the core, as illustrated in Figure 5c.

Figure 12. Output power, power loss, total current, and efficiency of ferrite transformerVˆ A at = Figure 12. OutputFigure 12. power, Output power power, loss, power total current, loss, total and current, efﬁciency an ofd efficiency ferrite transformer of ferrite Atransformer at p = 42, 48,A at and 54= V under the SPS modulation42, 48,m and= 1.0. 54 V under the SPS modulation m = 1.0.

Figure 13. Output power, power loss, total current, and efficiency of nanocrystalline transformer B Figure 13. Output power, power loss, total current, and efficiency of nanocrystalline transformerˆ B Figure 13. Output power, power loss, total current, and efﬁciency of nanocrystalline transformer B at Vp = 42, 48, and 54 V at = 42, 48, and 54 V under the SPS modulation m = 1.0. under the SPS modulation m = 1.0.

Figures 15–17 show the output power P2, and power loss Ploss of ferrite transformer A and nanocrystalline transformers B and C under the EPS modulation at Vˆp = 48 and 54 V with m = 0.7 to 1.0. The core loss Pf e of each operating condition is also given in the figures. The indicated core loss Pf e of the ferrite transformer is scaled to 70% of the measured core loss, due to the temperature-dependence. Core loss Pf e and the RMS current [28] decreases with the duty ratio m, which consequently raises the efficiency for all the transformers. It can be observed from the three transformers that the output power P2 at m = 0.9 curves are slightly lower than P2 at m = 1.0, as given in (3). The core loss Pf e reduction at from m = 1.0 to m = 0.9 is more pronounced than adjusting the duty ratio m at a lower value which can be observed from Figure 10. For control simplicity and enhanced efficiency, the DAB DC-DC converter can, therefore, be operated with the SPS modulation with a fixed duty ratio m = 0.9 in the primary voltage Vˆ . p Energies 2021, 14, x FOR PEER REVIEW 16 of 22

Energies 2021, 14, 2407 16 of 21 Energies 2021, 14, x FOR PEER REVIEW 16 of 22

Figure 14. Output power, power loss, total current, and efficiency of nanocrystalline transformer C at = 42, 48, and 54 V under the SPS modulation m = 1.0.

Figures 15–17 show the output power , and power loss of ferrite transformer A and nanocrystalline transformers B and C under the EPS modulation at = 48 and 54 V with m = 0.7 to 1.0. The core loss of each operating condition is also given in the figures. The indicated core loss of the ferrite transformer is scaled to 70% of the measured core loss, due to the temperature-dependence. Core loss and the RMS current [28] decreases with the duty ratio m, which consequently raises the efficiency for all the transformers. It can be observed from the three transformers that the output power at m = 0.9 curves are slightly lower than at m = 1.0, as given in (3). The core loss reduction at from m = 1.0 to m = 0.9 is more pronounced than adjusting the duty ratio m at

a lower value which can be observed from Figure 10. For control simplicity and enhanced Figure 14. Output power, power loss, total current, and efficiency of nanocrystalline transformerˆ C Figure 14. Outputefficiency, power, the powerDAB DC-DC loss, total converter current, and can, efﬁciency therefore, of nanocrystalline be operated with transformer the SPS Cmodulation at Vp = 42, 48, and 54 V under the SPSat modulation = 42, 48, andm = 54 1.0. V under the SPS modulation m = 1.0. with a fixed duty ratio m = 0.9 in the primary voltage .

FigureFigure 15. 15.Output Output power power and and efficiency efficiency of of ferrite ferrite transformer transformer A A at atVˆ p= 48 = 48 and and 54 54 V V with withm m= 0.7= 0.7 to to 1.0. 1.0. Figure 18 shows the thermal images of the MF transformers after being operated at the nominal power for one hour. The hottest section occurs at the winding of each transformer. Ferrite transformer A is hotter than the two nanocrystalline transformers, which agrees with the predicted loss in Table3. Table4 summarizes the test results of the three MF transformers. The calculated power density of each transformer includes the winding geometry. Although the toroidal nanocrystalline transformer C exhibits the highest power density and efficiency, its geometry makes it difficult to construct the windings, and a small parameter mismatch in the DAB DC-DC converter could lead to saturation in the core with limited prevention schemes. The C-core nanocrystalline transformer B is a good choice considering its power density, efficiency, winding manufacturing, and saturation management. Figure 4 indicates Figure 15. Outputthat power the and nanocrystalline efficiency of ferrite material tran forsformer transformer A at = B48 can and potentially 54 V with m operate = 0.7 to at frequencies 1.0. up to 100 kHz with core loss lower than the N87 ferrite, while the nanocrystalline material

Energies 2021, 14, 2407 17 of 21

for transformer C is optimized for operating at 20 kHz [31]. Ferrite is the best candidate for frequencies above 100 kHz. The test results of the prototype transformers with the DAB DC-DC converter are comparable with the literature. The authors of [19] calculated that an E100 3C90 ferrite transformer for a 400-V 20-kHz DAB DC-DC converter has an efficiency of 99.31% with a power density of 13 W/cm3. A Vitroperm500F transformer for a 120 V/240 V 5-kHz DAB DC-DC converter was tested at a partial load with an efficiency of 99.41% and power density of 15 W/cm3 [48]. However, it cannot be directly justified due to different operating conditions. The total core cost used in this study is also summarized in Table4. The E65 N87 ferrite cores for transformer A and the King Magnetics KMN503220T nanocrystalline cores for transformer C are manufactured in bulk and are commercially available at a low unit cost. Meanwhile, a small number of MK magnetics SC2043M1 nanocrystalline C-cores were ordered for this study only. The MK magnetics SC2043M1 nanocrystalline C-cores EnergiesEnergies 2021 2021, ,14 14, ,x x FOR FOR PEER PEER REVIEW REVIEW 1717 ofof 2222 would be competitive if manufactured in bulk.

Figure 16. Output power and efficiency of nanocrystalline transformer B at = 48 and 54 V with Figure 16.FigureOutput 16. Output power power and efﬁciency and efficiency of nanocrystalline of nanocrystalline transformer transformer B at Vˆ pB =at 48 and = 48 54 and V with 54 Vm with= 0.7 to 1.0. mm == 0.70.7 toto 1.0.1.0.

Figure 17. Output power and efficiency of nanocrystalline transformer ˆC at = 48 and 54 V with Figure 17.FigureOutput 17. Output power power and efﬁciency and efficiency of nanocrystalline of nanocrystalline transformer transformer C at V pC= at 48 and = 48 54 and V with 54 Vm with= 0.7 to 1.0. mm == 0.70.7 toto 1.0.1.0.

FigureFigure 1818 showsshows thethe thermalthermal imagesimages ofof thethe MFMF transformerstransformers afterafter beingbeing operatedoperated atat thethe nominalnominal powerpower forfor oneone hour.hour. TheThe hottesthottest sesectionction occursoccurs atat thethe windingwinding ofof eacheach trans-transformer.former. FerriteFerrite transformertransformer AA isis hotterhotter thanthan thethe twotwo nanocrystallinenanocrystalline transformers,transformers, whichwhich agreesagrees withwith thethe predictedpredicted lossloss inin TableTable 3.3.

Energies 2021, 14, 2407 18 of 21 Energies 2021, 14, x FOR PEER REVIEW 18 of 22

(a)

(b)

(c)

FigureFigure 18. Steady-stateSteady-state thermal thermal images images of ofthe the MF MF transformers transformers with with the DAB the DAB DC-DC DC-DC converter: converter: (a) Ferrite transformer A; (b) nanocrystalline C-core transformer B; (c) nanocrystalline toroidal trans- (a) Ferrite transformer A; (b) nanocrystalline C-core transformer B; (c) nanocrystalline toroidal former C. transformer C.

TableTable 4. Test 4 results summarizes of the prototype the test MFresults transformers. of the three MF transformers. The calculated power density of each transformer includes the winding geometry. Although the toroidal nanocrystalline transformer C exhibits the highest powerPrototype density Transformers and efficiency, its geom- Parameters etry makes it difficult to construct the windings,ABC and a small parameter mismatch in the DAB DC-DC converter could lead to saturation in the core with limited prevention Nominal power at 48 V 1054 W 1132 W 1170 W schemes.Maximum The power C-core at 54 nanocrystalline V transformer 1201 W B is a good choice 1277 W considering 1230 its power W density,Power density efficiency, winding manufacturing,6 W/cm and saturation3 9management. W/cm3 Figure12 W/cm 4 indi-3 catesPloss atthat nominal the nanocrystalline power material for 24.2transformer W B can 16.3 potentially W operate 17.3 at W fre- quenciesPf e at nominal up to 100 power kHz with core loss lower than 5.0 W the N87 ferrite, 3.5 while W the nanocrystalline 1.9 W materialη at nominal for transformer power C is optimized for 97.8% operating at 20 kHz 98.6% [31]. Ferrite is 98.5% the best candidateη with SPS, for 42–54 frequencies V, at m = above1.0 100 kHz. 97.6–98.5% 98.4–99.0% 98.5–99.1% η withThe EPS, testm results= 0.7 − of1.0, the at 48,prototype 54 V transformers 97.6–98.8% with the 98.4–99.1% DAB DC-DC converter 98.5–99.2% are Maximum temperature 78.5 ◦C 71.0 ◦C 60.1 ◦C comparable with the literature. The authors of [19] calculated that an E100 3C90 ferrite Total core cost 28 USD 250 USD 6 USD

Energies 2021, 14, 2407 19 of 21

6. Conclusions Three 20-kHz transformers were constructed on E65 N87 MnZn ferrite cores, 17-µm thick ribbon-wound nanocrystalline C cores, and a 20-µm thick ribbon-wound nanocrystalline toroid. Their experimental performances with a 1.1-kW 48 V/400 V DAB DC-DC converter were compared. The two nanocrystalline transformers exhibited better efﬁciency and power density with lower core loss and temperature rise compared to the ferrite transformer. A nanocrystalline transformer with the uncut toroid was found to offer better performance than the transformer with cut C-cores, since no deterioration occurred during the cutting process. The core loss of the ferrite transformer varies with core temperature, which is difﬁcult to design optimally. However, high permeability in the toroidal nanocrystalline transformer tended to saturate, due to a minor mismatch in circuit parameters. Considering the performance, saturation prevention, and winding manufacturing, cut nanocrystalline cores are suitable for transformers in DAB DC-DC converters with a switching frequency of up to 100 kHz. Ferrite material is a better choice for a switching frequency above 100 kHz. Furthermore, the difference between the calculated core loss, using the iGSE, and the measured core loss indicates that the core loss data for each core geometry should be provided to accurately design the transformer.

Author Contributions: Conceptualization, S.S., T.S. (Toshiro Sato) and V.C.; methodology, S.S.; software, S.S.; validation, S.S., A.P., P.N. and T.S. (Tawat Suriwong); formal analysis, S.S.; investigation, S.S.; resources, S.S.; data curation, S.S., A.P. and P.N.; writing—original draft preparation, S.S.; writing—review and editing, S.S.; visualization, S.S.; supervision, T.S. (Toshiro Sato) and V.C.; project administration, S.S.; funding acquisition, S.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Thailand Research Fund and the Office of the Higher Education Commission, Thailand, research grant number MRG6080051. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: Many thanks to Roy I. Morien and David James Sims for their editing assistance and advice on English expressions in this document. Conflicts of Interest: The authors declare no conflict of interest.

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